System and method for using combining couplers with asymmetric split ratios in a lidar system

ABSTRACT

A laser radar, or “lidar” system, employs an asymmetric single-ended detector to detect received signals reflected back from targets. The asymmetric single-ended detector benefits from a reduced part count and fewer optical splices while nearly achieving a same gain as a symmetric differential detector.

FIELD OF THE INVENTION

The invention is generally related to lidar system (i.e., laser radarsystems), and more particularly, using asymmetric split ratio combiningcouplers and single-ended detection.

BACKGROUND OF THE INVENTION

Various conventional lidar systems (i.e., laser radar systems) employcoherent detection, in which a received optical signal is combined witha mixing or reference optical signal, typically with a symmetriccombining coupler, to produce an interference signal. A symmetriccombining coupler is a combining coupler with a power transfer ratio of50% between its two output ports (i.e., each port receives 50% of theoutput power from the combing coupler).

In some conventional systems, the interference signal from a single portof the symmetric combining coupler is applied to a detector to produce adetected signal. This is referred to as single-ended detection. Becausethe two ports of the symmetric combining coupler each produce aninterference signal with a 180-degree phase difference from one another,these two interference signals may be combined to produce a differentialsignal that can subsequently be applied to a detector to produce adetected signal. This is referred to as differential detection.

Optical systems employing single-ended detection typically employ fewerdetectors and require fewer optical fiber splices. However, such opticalsystems employing single-ended detection experience a 3 dB loss insignal-to-noise ratio (SNR) over those employing differential detection.Because of this, optical systems that require higher sensitivity (suchas lidar systems) typically employ differential detection with symmetriccombining couplers rather than single-ended detection.

What is needed is a lidar system that employs single-ended detectionthat does not suffer the SNR losses of conventional systems.

SUMMARY OF THE INVENTION

According to various implementations of the invention, a laser radar, or“lidar” system, employs an asymmetric single-ended detector to detectreceived signals reflected back from targets. The asymmetricsingle-ended detector benefits from a reduced part count (as comparedwith a differential detector) and fewer optical splices while achievingnearly a same gain as a symmetric differential detector.

Various implementations of the invention are directed toward a lidarsystem that includes a laser source configured to generate a laseroutput; a splitter configured to split the laser output into a transmitsignal and a mixing signal; and a single-ended detector comprising: anasymmetric combiner configured to combine a received signal and themixing signal and output a combined signal, wherein the received signalis a reflected portion of the transmit signal reflected back from atarget and received by the lidar, wherein the asymmetric combiner has asplit ratio greater than 0.5, and a detector configured to detect thecombined signal.

Various implementations of the invention are directed toward a methodfor detecting a reflected signal from a target, the method comprising:receiving the reflected signal from the target; combining the receivedsignal with a mixing signal using an asymmetric combiner having a splitratio greater than 0.5 to generate a combined signal; and detecting thecombined signal using a single-ended detector.

These implementations, their features and other aspects of the inventionare described in further detail below.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a conventional symmetric single-ended detector.

FIG. 2 illustrates a conventional symmetric double-ended detector.

FIG. 3 illustrates a lidar system (i.e., laser radar) according tovarious implementations of the invention.

FIG. 4 illustrates a relationship between e-Field inputs and outputs fora combining coupler having a split ratio, σ.

FIG. 5 illustrates respective scaling factors between e-Field inputs andoutputs form a combining coupler having a split ratio, σ.

FIG. 6 illustrates gain curves for a single-ended detector in comparisonwith a differential detector as a function of split ratio, FIG. 4illustrates a relationship between e-Field inputs and outputs from acombining coupler having a split ratio, σ.

DETAILED DESCRIPTION

As discussed above, conventional lidar systems that employ single-endeddetection use fewer receive detectors and require fewer fiber-opticsplices than their double-ended, differential detection counterparts;however, detection in such conventional lidar system experiences a 3 dBloss in signal-to-noise ratio (SNR) in relation to conventional lidarsystems that employ differential detection. According to variousimplementations of the invention, asymmetric combining couplers may beused in a lidar system employing single-ended detection to substantiallyreduce these losses in SNR. Moreover, in various implementations of theinvention, use of the asymmetric combining couplers does not increasethe cost of parts or labor, or increase package size in comparison withconventional single-ended detection systems.

According to various implementations of the invention, an asymmetriccombining coupler with an asymmetric split ratio between its outputports (e.g., 80%/20%, 90%/10%, etc.) may be used in the lidar system. Inorder to fully recognize the gains (i.e., increased sensitivity,improvement in SNR, etc.) of the asymmetric combining couplers in suchsystems, a power level of a reference signal (also referred to as amixing signal) may be adjusted in relation to the asymmetric split ratioused.

Before discussing various implementations of the invention, conventionaldetectors are first described. FIG. 1 illustrates a conventionalsymmetric single-ended detector 100. Symmetric single-ended detector 100includes an optical mixing signal 110 (sometimes referred to herein asan “LO signal”) and a received optical signal 120 (typically reflectedfrom a target as would be appreciated). Depending on the application,optical mixing signal 110 may be a time-shifted (i.e., time-delayed)version of an actual transmit signal as would be appreciated. Receivedoptical signal 120 and optical mixing signal 110 may be mixed together,for example, via a coupler having a symmetric split ratio (e.g., 50/50)such as a coupler 130. An output 140 of coupler 130 is applied to anelectro-optical detector 150, which as illustrated may be a PIN diode.Detector 150 converts optical power (e.g., from coupler 130) to anelectrical current 160 as would be appreciated. Current 160 may besubsequently measured as would be appreciated.

FIG. 2 illustrates a conventional symmetric double-ended detector 200.Symmetric double-ended detector 200 includes an optical mixing signal110 (which, again, may be a time-shifted version of the transmit signal)and a received optical 120. Received optical signal 120 and opticalmixing signal 110 may be mixed together, for example, via a couplerhaving a symmetric split ratio (e.g., 50/50) such as coupler 130. Withdetector 200, both outputs 240 (illustrated as an output 240A and anoutput 240B) of coupler 130 are applied to electro-optical detectors 250(illustrated as an electro-optical detector 250A and an electro-opticaldetector 250B). Detectors 250A, 250B convert optical power to electricalcurrents 260A, 260B, respectively, which may be subsequently measured aswould be appreciated. Creating a difference signal between these twocurrents typically realizes a sensitivity gain of 3 dB over thesingle-ended detector 100 as would be appreciated.

A simple lidar system employing asymmetric detection is now described inaccordance with various implementations of the invention. FIG. 3illustrates a lidar system 300 (i.e., laser radar) according to variousimplementations of the invention. Lidar system 300 includes a coherentlaser source 310 that outputs an optical signal 315, which in turnpropagates to a splitting coupler 320. Splitting coupler 320 splitsoutput optical signal 315 into two components, a transmit signal 325 anda mixing signal 326 (i.e., an LO signal).

Transmit signal 325 propagates through a optical separator 330 onto afiber tip 340, from which it transitions into free space, is focused bya lens system 350 onto a target 360 and reflected back as a reflectedsignal. The reflected signal follows a path back in the oppositedirection through lens system 350 and fiber tip 340 and back to opticalseparator 330.

Optical separator 330 separates transmit signal 325 from the reflectedsignal and outputs a receive signal 336. In various implementations ofthe invention, optical separator 330 may be a circulator, a splitter, orother suitable optical separator that separates transmit signal 325 fromthe reflected signal as would be appreciated.

Receive signal 336 and mixing signal 326 are combined by a combiningcoupler 370 to output a combined signal 375. In some implementations ofthe invention, a gain or attenuation stage (not otherwise illustrated)may be applied to mixing signal 326 prior to reaching combining coupler370 in order to adjust mixing signal 326 to an anticipated power levelof receive signal 336 as would be appreciated. According to variousimplementations of the invention, combining coupler 370 is single-endedand utilizes an asymmetric split ratio as discussed in further detailbelow.

Combined signal 375 is provided to a detector 380 to convert thecombined signal 375 to an electrical signal for measurement as would beappreciated.

More complex lidar systems may benefit from various implementations ofthe invention as would be appreciated. For example, in someimplementations of the invention, lidar system 300 may be incorporatedinto a dual laser source, chirped coherent laser radar system capable ofunambiguously and simultaneously measuring both range and Dopplervelocity of a point on target 360. Such a laser radar system isdescribed in U.S. Pat. No. 8,582,085 entitled “Chirped Coherent LaserRadar with Multiple Simultaneous Measurements,” which is incorporatedherein by reference in its entirety.

The amplitudes of noise power and signal power under certain conditionsare derived for both conventional symmetric single-ended detector 100and conventional symmetric differential detector 200 and are nowdescribed. Afterwards, an effect of varying the split ratio of combiningcoupler 370 is explored.

For purposes of this discussion, the signal-to-noise ratio (SNR) of theelectrical output of a detector is described as the power of thecomponent with the frequency difference of LO and Rx signals relative tothe noise power in a given receive bandwidth. To explore the effect ofvarying the split ratio of combining coupler 370 on the resulting SNR ofthe output of detector 380, an analytical expression for the fieldstrength at a detector surface and the resulting detector current isderived. Absolute values of noise levels or SNR are not of interesthere, but rather the relative gain or loss of SNR relative to asymmetric coupler (i.e., a couple having a split ratio of 0.5 or“50/50”). Because relative gains are calculated, physical constants andtheir associated units are omitted.

For illustrative purposes, this derivation of relative SNR is based onthe following assumptions:

-   -   The receive signal (i.e., Rx signal) is of substantially lower        power than the transmit signal (i.e., LO signal). Therefore, the        noise power density at the detector output is determined only by        the fraction of optical power from the LO signal reaching the        detector surface.    -   The detector is not saturated, i.e. the optical power on the        detector surface is within the limits of linear operation of the        detector.    -   Detector shot noise is the only significant contributor to the        overall noise level, all other noise sources are negligible.    -   The detector converts optical power to a current within a        bandwidth significantly lower than the optical frequency. All        frequency components of the optical power at the optical        frequency or its multiples are averaged by the detector; only        components at differences of optical frequencies are propagated        as the signal to be detected.

With these assumptions, the electrical component of the optical LOsignal electromagnetic field (i.e., E-field) may be described as:

LO(t)=E _(LO)*cos(ω_(LO)(t)*t+φ _(LO))

where

-   -   E_(LO) denotes the field strength;    -   ω_(LO)(t) is the time-varying optical frequency of the LO        signal; and    -   φ_(LO) is the LO signal phase at t=0.        Similarly, the receive signal may be described as:

Rx(t)=E _(Rx)*cos(ω_(Rx)(t)*t+φ _(Rx))

where

-   -   E_(Rx) denotes the field strength;    -   ω_(Rx)(t) is the time-varying optical frequency of the Rx        signal; and    -   φ_(Rx) is the Rx signal phase at t=0.

Symmetric coupler 130 is a reciprocal and symmetric four-port devicewhich exhibits a power split ratio, σ, between its two inputs E₁, E₂ andits two outputs E₃, E₄ as illustrated in FIG. 4. The E-fields of theoptical inputs are propagated according to the following transfermatrix:

${\begin{matrix}E_{3} \\E_{4}\end{matrix}} = {{\begin{matrix}\sqrt{1 - \sigma} & {{- j}*\sqrt{\sigma}} \\{{- j}*\sqrt{\sigma}} & \sqrt{1 - \sigma}\end{matrix}}*{\begin{matrix}E_{1} \\E_{2}\end{matrix}}}$

In many applications of these couplers, only three of the four ports areused and the unconnected port is terminated to eliminate backreflection. In such applications the split ratio of the ports on oneside relative to the one port on the other side is indicated as apercentage such as illustrated in FIG. 5.

For single-ended detectors, the power split ratio of a given coupler isσ, where 0<σ<1. For symmetric couplers, σ=0.5; whereas for asymmetriccouplers, (e.g., σ< >0.5), the power from the Rx input reaching thedetector is scaled by σ; and the power from the LO input reaching thedetector is scaled by 1−σ. The starting phases φ_(LO) and φ_(Rx) arearbitrary because the phase at t=0 depends on the location of themeasurement.

The electrical field strength of the optical signal at the output of thecoupler connected to the detector may be expressed as:

E ₁ =√{square root over (σ)}*E _(Rx)*sin(ω_(Rx)(t)*t+φ _(Rx))+√{squareroot over (1−σ)}*E _(LO)*cos(ω_(LO)(t)*t+φ _(LO))

As indicated, both components E_(Rx) and E_(LO) are scaled with thesquare root of the respective split ratio (i.e., either the square rootof σ or the square root of 1−σ). The detector current is proportional tothe square of this field strength.

I ₁ =η*E ₁ ²

The proportionality factor η contains the detector efficiency, amongother constants. Only the SNR change relative to split ratio is ofinterest; the detector efficiency does not affect this ratio and isomitted in the following equations.

After squaring the expression for E₁ and rearranging with trigonometricidentities, the detector current can be expressed as:

$I_{1} \sim {{\frac{\sigma}{2}*E_{Rx}^{2}*\left( {1 - {\cos \left( {{2*{\omega_{Rx}(t)}*t} + {2*\phi_{Rx}}} \right)}} \right)} + {\frac{1 - \sigma}{2}*E_{LO}^{2}*\left( {1 + {\cos \left( {{2*{\omega_{LO}(t)}*t} + {2*\phi_{LO}}} \right)}} \right)} + {\sqrt{\sigma - \sigma^{2}}*E_{Rx}*E_{LO}*{\sin \left( {{\left( {{\omega_{Rx}(t)} - {\omega_{LO}(t)}} \right)*t} + \phi_{Rx} - \phi_{LO}} \right)}} + {\sqrt{\sigma - \sigma^{2}}*E_{Rx}*E_{LO}*{\sin \left( {{\left( {{\omega_{Rx}(t)} + {\omega_{LO}(t)}} \right)*t} + \phi_{Rx} + \phi_{LO}} \right)}}}$

The first term is the contribution of the receive power and isnegligible due to the assumption of low receive signal power. The secondterm is the main contribution to the total detector power from the LOsignal; the shot noise power density of the resulting electrical currentscales with the square root of this power. The third term is the mixingproduct with the frequency difference between Rx and LO inputs. Thisterm is in a frequency range detectable by the detector and is convertedinto the electrical receive signal. The fourth term describes a signalat twice the optical frequency; since it does not produce an averagecurrent and is proportional to the receive field strength, itscontribution to the total detector power is negligible.

The detector will average all frequency components at optical frequencyor above and the detector current then may be expressed as:

$I_{1} \sim {{\frac{\sigma}{2}*E_{Rx}^{2}} + {\frac{1 - \sigma}{2}*E_{LO}^{2}} + {\sqrt{\sigma - \sigma^{2}}*E_{Rx}*E_{LO}*{\sin \left( {{\left( {{\omega_{Rx}(t)} - {\omega_{LO}(t)}} \right)*t} + \phi_{Rx} - \phi_{LO}} \right)}}}$

and the resulting contribution to the detector current by average poweron the detector surface is therefore given by:

$I_{avg} \sim {\frac{1 - \sigma}{2}*E_{LO}^{2}}$

To arrive at an SNR expression relative to the case of the symmetriccoupler (σ=0.5), the shot noise power and therefore the average detectorcurrent are held constant by adjusting the power of the LO signalaccording to the split ratio. The square of the field strength of the LOsignal for symmetric split ratio is denoted as N_(LO) ² and given by:

${I_{avg} \sim {0.25*N_{LO}^{2}}} = {\frac{1 - \sigma}{2}*E_{LO}^{2}}$

Expressing the LO power supplied to the coupler in terms of split ratiowhile keeping the average detector current constant yields:

$E_{LO} = {\frac{1}{\sqrt{2*\left( {1 - \sigma} \right)}}*N_{LO}}$

The receive signal of interest is given by the third term in theequation for detector current:

I _(sig)˜+√{square root over (σ−σ²)}*E _(Rx) *E_(LO)*sin((ω_(Rx)(t)−ω_(LO)(t))*t+φ _(Rx)−φ_(LO))

Accounting for the adjustment of LO power depending on split ratio, thesignal current will then become

$I_{sig} \sim {{+ \sqrt{\sigma - \sigma^{2}}}*E_{Rx}*\frac{1}{\sqrt{2*\left( {1 - \sigma} \right)}}*N_{LO}*{\sin \left( {{\left( {{\omega_{Rx}(t)} - {\omega_{LO}(t)}} \right)*t} + \phi_{Rx} - \phi_{LO}} \right)}}$

and after some simplification:

$I_{sig} \sim {{+ \sqrt{\frac{\sigma}{2}}}*E_{Rx}*N_{LO}*{\sin \left( {{\left( {{\omega_{Rx}(t)} - {\omega_{LO}(t)}} \right)*t} + \phi_{Rx} - \phi_{LO}} \right)}}$

with the RMS amplitude

${\left. I_{sig\_ RMS} \right.\sim\sqrt{\frac{\sigma}{2}}}*E_{Rx}*N_{LO}$

Shot noise current density in the electrical signal is proportional tothe square root of the average detector current; multiplying with thesquare root of some fixed receive bandwidth yields the noise currentmagnitude:

I _(noise) _(—) _(RMS)=√{square root over (2*q*I _(avg) *Bw)}

where q is the elementary charge and Bw is the receive bandwidth.

Inserting the equation for average current and ignoring the constant 2*qgives:

${\left. {I_{{noise\_ RM}S}(\sigma)} \right.\sim\frac{N_{LO}}{2}}*\sqrt{B\; w}$

The RMS noise current is not depending on split ratio which is expected,because LO power level was adjusted for average noise current to beindependent of split ratio.

${{SNR}(\sigma)} = {10*{\left. {\log_{10}\left( \frac{I_{sig\_ RMS}^{2}}{I_{noise\_ RMS}^{2}} \right)} \right.\sim 10}*{{\log_{10}\left( {\sigma*E_{Rx}^{2}*\frac{1}{B\; w}} \right)}\lbrack{dB}\rbrack}}$

The ratio of signal amplitudes over split ratio given constant noisepower translates directly to the SNR dependency in dB on split ratiorelative to σ=0.5:

SNR_(rel)(σ)=SNR(σ)−SNR(0.5)=10*log₁₀(2*σ)[dB]

For differential detectors, the power split ratio of the coupler is σ,where 0<σ<1; for symmetric couplers σ=0.5. For asymmetric couplers, thepower from the Rx input reaching a first detector is scaled by σ and thepower from the LO input reaching the first detector is scaled by 1−σ.These scaling factors are reversed for the second detector, i.e., thepower from the Rx input reaching the second detector is scaled by 1−σand the power from the LO input reaching the second detector is scaledby σ. Again, the starting phases are arbitrary.

The electrical field strength of the optical signal at the output of thecoupler connected to the detector generating current I₁ (e.g., current260B in FIG. 2) may be expressed as:

E ₁ =√{square root over (σ)}*E _(Rx)*sin(ω_(RX)(t)*t+φ _(Rx))+√{squareroot over (1−σ)}*E _(LO)*cos(ω_(LO)(t)*t+φ _(LO))

and the optical field strength contained in the output of the couplerconnected to the detector generating current I₂ (e.g., current 260A inFIG. 2) may be expressed as:

E ₂=√{square root over (1−σ)}*E _(Rx)*cos*(ω_(Rx)(t)*t+φ _(Rx))+√{squareroot over (σ)}*E _(LO)*sin(ω_(LO)(t)*t+φ _(LO))

The dependency of I₁ on E_(LO) and E_(Rx) is identical to the resultderived for the single-ended case and given by:

$\begin{matrix}{{{\left. I_{1} \right.\sim\frac{\sigma}{2}}*E_{Rx}^{2}*\left( {1 - {\cos \left( {{2*{\omega_{Rx}(t)}*t} + {2*\phi_{Rx}}} \right)}} \right)} + {\frac{1 - \sigma}{2}*E_{LO}^{2}*\left( {1 + {\cos \left( {{2*{\omega_{LO}(t)}*t} + {2*\phi_{LO}}} \right)}} \right)} + {\sqrt{\sigma - \sigma^{2}}*E_{Rx}*E_{LO}*{\sin \left( {{\left( {{\omega_{Rx}(t)} - {\omega_{LO}(t)}} \right)*t} + \phi_{Rx} - \phi_{LO}} \right)}} + {\sqrt{\sigma - \sigma^{2}}*E_{Rx}*E_{LO}*{\sin \left( {{\left( {{\omega_{Rx}(t)} + {\omega_{LO}(t)}} \right)*t} + \phi_{Rx} + \phi_{LO}} \right)}}} & \;\end{matrix}$

The dependency of I₂ on E_(LO) and E_(Rx) is arrived at by squaring theexpression for E₂:

$\begin{matrix}{{{\left. I_{2} \right.\sim\frac{1 - \sigma}{2}}*E_{Rx}^{2}*\left( {1 + {\cos \left( {{2*{\omega_{Rx}(t)}*t} + {2*\phi_{Rx}}} \right)}} \right)} + {\frac{\sigma}{2}*E_{LO}^{2}*\left( {1 - {\cos \left( {{2*{\omega_{LO}(t)}*t} + {2*\phi_{LO}}} \right)}} \right)} - {\sqrt{\sigma - \sigma^{2}}*E_{Rx}*E_{LO}*{\sin \left( {{\left( {{\omega_{Rx}(t)} - {\omega_{LO}(t)}} \right)*t} + \phi_{Rx} - \phi_{LO}} \right)}} + {\sqrt{\sigma - \sigma^{2}}*E_{Rx}*E_{LO}*{\sin \left( {{\left( {{\omega_{Rx}(t)} + {\omega_{LO}(t)}} \right)*t} + \phi_{Rx} + \phi_{LO}} \right)}}} & \;\end{matrix}$

The first terms are the contribution of the receive power and arenegligible due to the assumption of low receive signal power. The secondterms are the main contribution to the total detector power from the LOsignal; the shot noise power densities of the resulting electricalsignals scale with the square root of these powers. The third terms arethe mixing products with the frequency difference between Rx and LOinputs. These terms are in a frequency range detectable by the PIN diodeand their difference is converted into the electrical receive signal.The fourth terms describe signals at twice the optical frequency.Because these fourth terms do not produce an average current and areproportional to the receive field strength, their contributions to thetotal detector power are negligible.

The detectors will average all frequency components at optical frequencyor above and the detector currents may be expressed as:

${{\left. I_{1} \right.\sim\frac{\sigma}{2}}*E_{Rx}^{2}} + {\frac{1 - \sigma}{2}*E_{LO}^{2}} + {\sqrt{\sigma - \sigma^{2}}*E_{Rx}*E_{LO}*{\sin \left( {{\left( {{\omega_{Rx}(t)} - {\omega_{LO}(t)}} \right)*t} + \phi_{Rx} - \phi_{LO}} \right)}}$${{\left. I_{2} \right.\sim\frac{1 - \sigma}{2}}*E_{Rx}^{2}} + {\frac{\sigma}{2}*E_{LO}^{2}} - {\sqrt{\sigma - \sigma^{2}}*E_{Rx}*E_{LO}*{\sin \left( {{\left( {{\omega_{Rx}(t)} - {\omega_{LO}(t)}} \right)*t} + \phi_{Rx} - \phi_{LO}} \right)}}$

and the resulting contribution to the detector currents by average poweron the detector surface may therefore be expressed as:

${\left. I_{{avg}\; 1} \right.\sim\frac{1 - \sigma}{2}}*E_{{LO}}^{2}$${\left. I_{{{avg}\; 2}\;} \right.\sim\frac{\sigma}{2}}*E_{{LO}}^{2}$

Shot noise current density in the electrical signals is proportional tothe square root of the average detector currents:

I _(noise) _(—) _(RMS)=√{square root over (2*q*I _(avg) *Bw)}

where q is the elementary charge and Bw is the receive bandwidth.Because the shot noise contributions of both detectors are mutuallyuncorrelated, the noise power of both detectors may be added to derivethe resulting noise current of the differential arrangement for a givenbandwidth. This yields the following dependence on split ratio:

I _(noise) _(—) _(RMS) _(—) _(DIFF)(σ)·√{square root over (2*σ+2*σ²)}*E_(LO) *√{square root over (Bw)}

The amplitudes of the receive signal of interested are given by thethird term in the equations for detector current:

I _(sig1)˜+√{square root over (σ−σ²)}*E _(Rx) *E_(LO)*sin((ω_(Rx)(t)−ω_(LO)(t))*t+φ _(Rx)−φ_(LO))

I _(sig2)˜−√{square root over (σ−σ²)}*E _(Rx) *E_(LO)*sin((ω_(Rx)(t)−ω_(LO)(t))*t+φ _(Rx)−φ_(LO))

(46) As noted above, the detection circuit determines the difference ofthe two currents, effectively doubling the amplitude of the signalcurrent which may be expressed as:

I _(sig) _(—) _(DIFF) =I _(sig1) −I _(sig2)˜2*√{square root over(σ−σ²)}*E _(Rx) *E _(LO))*sin((ω_(Rx)(t)−ω_(LO)(t))*t+φ _(Rx)−φ_(LO))

with the RMS amplitude

I _(sig) _(—) _(RMS) _(—) _(DIFF)˜√{square root over (2)}*√{square rootover (σ−σ²)}*E _(Rx) *E _(LO)

Unlike the scenario of single-ended detection, the LO power is keptconstant. For asymmetric split ratios, the total shot noise power levelis taken into account. The SNR dependence on split ratio may beexpressed as:

${{SNR}(\sigma)} = {10*{\left. {\log_{10}\left( \frac{I_{{sig\_ RMS}{\_ DIFF}}^{2}}{I_{{noise\_ RMS}{\_ DIFF}}^{2}} \right)} \right.\sim 10}*{\log_{10}\left( {\frac{2*\left( {\sigma - \sigma^{2}} \right)}{1 - {2*\sigma} + {2*\sigma^{2}}}*E_{Rx}^{2}*\frac{1}{B\; w}} \right)}}$

SNR dependency on split ratio relative to σ=0.5 for differentialdetection may then be expressed as:

${{SNR}_{rel}(\sigma)} = {{{{SNR}(\sigma)} - {{SNR}(0.5)}} = {10*\log_{10}{\frac{2*\left( {\sigma - \sigma^{2}} \right)}{1 - {2*\sigma} + {2*\sigma^{2}}}\lbrack{dB}\rbrack}}}$

For purposes of comparing detector efficiency in both architectures, theSNR dependence on split ratio for a given receive bandwidth may derived.As the calculations above show, SNR does not depend on LO power level aslong as the assumptions stated at the beginning are valid.

The derivations of SNR for both architectures above gave the followingresults under identical neglect of proportionality constants (andphysical units):

${Single}\text{-}{Ended}\text{:}\mspace{14mu} {\left. {{SNR}(\sigma)} \right.\sim 10}*{\log_{10}\left( {\sigma*E_{Rx}^{2}*\frac{1}{B\; w}} \right)}$${Differential}\text{:}\mspace{14mu} {\left. {{SNR}(\sigma)} \right.\sim 10}*{\log_{10}\left( {\frac{2*\left( {\sigma - \sigma^{2}} \right)}{1 - {2*\sigma} + {2*\sigma^{2}}}*E_{Rx}^{2}*\frac{1}{B\; w}} \right)}$

The single-ended case with σ=0.5 yields:

${\left. {{SNR}(0.5)} \right.\sim 10}*{\log_{10}\left( {0.5*\frac{E_{Rx}^{2}}{B\; w}} \right)}$

Expressing both SNR equations relative to the single-ended case withσ=0.5 yields:

Single-Ended:  SNR_(rel_SE)(σ) = 10 * log  10(2 * σ)${{Differential}\text{:}\mspace{14mu} {{SNR}_{rel\_ DE}(\sigma)}} = {10*\log \; 10\left( \frac{4*\left( {\sigma - \sigma^{2}} \right)}{1 - {2*\sigma} + {2*\sigma^{2}}} \right)}$

FIG. 6 illustrates the relative SNR for both a single-ended detector anda differential detector over varying split ratios, σ. As illustrated,the relative SNR gain of differential detection over single-endeddetection with a symmetric coupler is 3 dB. This is expected asdifferential detection adds signal amplitudes, equivalent to quadruplingthe signal power, while the noise contributions of both coupler outputsare added in power, not amplitude. As also illustrated, the relative SNRgain of single-ended detection continues to increase with the increaseof the split ratio until at an approximate split ratio, σ=0.8, thedifference in gain between such a single-ended asymmetric detector and asymmetric differential detector is only roughly 1 dB; and at anapproximate split ratio, σ=0.9, this difference in gain is even furtherreduced. Experimental results confirmed this analysis and the attendantassumptions.

Various implementations of the invention utilize asymmetric single-endeddetection with a combining coupler 370 having a split ratio, σ>0.5.Various implementations of the invention utilize asymmetric single-endeddetection with a combining coupler 370 having a split ratio, σ>0.6.Various implementations of the invention utilize asymmetric single-endeddetection with a combining coupler 370 having a split ratio, σ>0.7.Various implementations of the invention utilize asymmetric single-endeddetection with a combining coupler 370 having a split ratio, σ>0.8.Various implementations of the invention utilize asymmetric single-endeddetection with a combining coupler 370 having a split ratio, σ>0.9.Various implementations of the invention utilize asymmetric single-endeddetection with a combining coupler 370 having an empirical split ratio,σ=0.7. Various implementations of the invention utilize asymmetricsingle-ended detection with a combining coupler 370 having an empiricalsplit ratio, σ=0.8. Various implementations of the invention utilizeasymmetric single-ended detection with a combining coupler 370 having anempirical split ratio, σ=0.9.

While the invention has been described herein in terms of variousimplementations, it is not so limited and is limited only by the scopeof the following claims, as would be apparent to one skilled in the art.These and other implementations of the invention will become apparentupon consideration of the disclosure provided above and the accompanyingfigures. In addition, various components and features described withrespect to one implementation of the invention may be used in otherimplementations as well.

What is claimed is:
 1. A lidar comprising: a laser source configured togenerate a laser output; a splitter configured to split the laser outputinto a transmit signal and a mixing signal; and a single-ended detectorcomprising: an asymmetric combiner configured to combine a receivedsignal and the mixing signal and output a combined signal, wherein thereceived signal is a reflected portion of the transmit signal reflectedback from a target and received by the lidar, wherein the asymmetriccombiner has a split ratio greater than 0.5, and a detector configuredto detect the combined signal.
 2. The lidar of claim 1, wherein theasymmetric combiner has a split ratio greater than or equal to 0.6. 3.The lidar of claim 1, wherein the asymmetric combiner has a split ratiogreater than or equal to 0.7.
 4. The lidar of claim 1, wherein theasymmetric combiner has a split ratio greater than or equal to 0.8. 5.The lidar of claim 1, wherein the asymmetric combiner has a split ratiogreater than or equal to 0.9.
 6. The lidar of claim 1, wherein theasymmetric combiner has an empirical split ratio of 0.8.
 7. The lidar ofclaim 1, wherein the asymmetric combiner has an empirical split ratio of0.9.
 8. The lidar of claim 1, wherein the asymmetric combiner comprisesan asymmetric combining coupler.
 9. The lidar of claim 1, wherein thedetector comprises a PIN diode.
 10. The lidar of claim 1, furthercomprising a gain stage or an attenuation stage configured to adjust apower level of the mixing signal prior to input to the asymmetriccombiner.
 11. A method for detecting a reflected signal from a target,the method comprising: receiving the reflected signal from the target;combining the received signal with a mixing signal using an asymmetriccombiner having a split ratio greater than 0.5 to generate a combinedsignal; and detecting the combined signal using a single-ended detector.12. The method of claim 11, wherein the asymmetric combiner has a splitratio greater than or equal to 0.6.
 13. The method of claim 11, whereinthe asymmetric combiner has a split ratio greater than or equal to 0.7.14. The method of claim 11, wherein the asymmetric combiner has a splitratio greater than or equal to 0.8.
 15. The method of claim 11, whereinthe asymmetric combiner has a split ratio greater than or equal to 0.9.16. The method of claim 11, wherein the asymmetric combiner has anempirical split ratio of 0.8.
 17. The method of claim 11, wherein theasymmetric combiner has an empirical split ratio of 0.9.